Bifurcations of relaxation oscillations

We are still far from a comprehensive theory of bifurcation in dynamical systems with multiple time scales. However, systematic application of geometric methods and study of examples have produced descriptions of varied phenomena. These lectures present a selective summary of some of what has been discovered, concentrating on periodic orbits called relaxation oscillations. We focus upon key aspects of the phenomena, avoiding mathematical details and making the analysis as simple as possible. The dynamics of reduced systems plays a central role in our discussion.